REMIND - REgional Model of INvestments and Development

2.1.3

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Growth (20_growth)

Description

The growth module decides whether to follow a quasi exogenous growth path(calibrated to SSP GDP paths) or an endogenous growth path that includes innovation, immitation and spillover effects

Interfaces

Interfaces to other modules
Interfaces to other modules

Input

module inputs (A: exogenous | B: spillover)
  Description Unit A B
cm_startyear first optimized modelling time step \(year\) x
pm_cesdata
(tall, all_regi, all_in, cesParameter)
parameters of the CES function x x
pm_cumEff
(tall, all_regi, all_in)
parameter for spillover externality (aggregated productivity level) x
pm_ts
(tall)
(t_n+1 - t_n-1)/2 for a timestep t_n x
pm_ttot_val
(ttot)
value of ttot set element x
vm_cesIO
(tall, all_regi, all_in)
Production factor x
vm_invImi
(ttot, all_regi, all_in)
Investment into imitation x x
vm_invInno
(ttot, all_regi, all_in)
Investment into innovation x x
vm_invMacro
(ttot, all_regi, all_in)
Investment for capital for ttot x
vm_invRD
(ttot, all_regi, all_in)
R&D investments x

Output

module outputs
  Description Unit
vm_effGr
(ttot, all_regi, all_in)
growth of factor efficiency

Realizations

(A) exogenous

The exogenous growth realization makes no changes to the (macroeconomic) efficiency growth rate parameters. In effect, it leaves all respective parameter specifications to be dealt with by the calibration (usually to given SSP GDP paths) and loading in module 29_CES_parameters, respectively.

Limitations Apart from variation of exogenous GDP scenarios, the model can (in contrast to the endogenous/spillover realization) only slightly correct growth paths in reaction of policy shocks. This correction is done by an adjustment of capital accumulation.

(B) spillover

This realization implies an endogenous growth path. It replaces and overwrites, respectively, the exogenous SSP GDP growth paths. The spillover module computes new efficiency growth parameters for labor and energy that enter the upper level of the CES production function. The implemented growth engine allows to increase growth by R&D investments into innovation and imitation. It also allows for spillover effects that represent the catch-up with technological frontier. The model implemented as well as its parameetrization is based on Huebler et al. (2012).

\[\begin{multline*} vm\_effGr(ttot+1,regi,inRD20) = \left(1 + \left(p20\_coef\_H(ttot,regi) \cdot p20\_coef\_EL(inRD20) \cdot \left(v20\_effInno(ttot,regi,inRD20) + v20\_effImi(ttot,regi,inRD20)\right) \cdot \frac{vm\_invMacro(ttot,regi,"kap")}{\left(vm\_cesIO(ttot+1,regi,"kap")+0.00001\right)}\right)\right)^{\left(\frac{pm\_ts(ttot)}{5}\right) } \cdot vm\_effGr(ttot,regi,inRD20) \end{multline*}\]

\[\begin{multline*} v20\_effInno(ttot,regi,inRD20) = p20\_coeffInno \cdot \left(\frac{vm\_invInno(ttot,regi,inRD20) }{\left(pm\_cesdata(t,regi,inRD20,"eff") \cdot vm\_effGr(ttot,regi,inRD20) + 0.00001\right)}\right)^{p20\_exponInno(ttot,regi,inRD20) }+ p20\_constRD \end{multline*}\]

\[\begin{multline*} v20\_effImi(ttot,regi,inRD20) = p20\_coeffImi \cdot \left(\frac{vm\_invImi(ttot,regi,inRD20)}{\left(pm\_cesdata(t,regi,inRD20,"eff") \cdot vm\_effGr(ttot,regi,inRD20) + 0.00001\right)}\right)^{p20\_exponImi(ttot,regi,inRD20) } \cdot \frac{ \left(\sum_{ regi2}\left(pm\_cesdata(t,regi2,inRD20,"eff") \cdot vm\_effGr(ttot,regi2,inRD20)\right) + pm\_cumEff\left(ttot,regi, inRD20\right)\right)}{ \left(pm\_cesdata(t,regi,inRD20,"eff") \cdot vm\_effGr(ttot,regi,inRD20) + 0.0001\right)} \end{multline*}\]

Limitations This realization was last applied with REMIND version 1.6, but not yet with REMIND2.0. In order to work properly it might be necessary to resolve interference with the calibration and module 29_CES_parameters.

Definitions

Objects

module-internal objects (A: exogenous | B: spillover)
  Description Unit A B
o20_ImiGDP_E share of imitation RD on GDP x
o20_ImiGDP_lab share of imitation RD on GDP x
o20_InnoGDP_E sahre of Innovation RD on GDP x
o20_InnoGDP_lab share of innovation RD on GDP x
p20_coef_EL
(all_in)
coefficient of RD function x
p20_coef_H
(ttot, all_regi)
human capital coefficient of RD function x
p20_coeffImi coefficient of Innovation RD investments x
p20_coeffInno coefficient of Innovation RD investments x
p20_constRD RD constant x
p20_dataeffscal_avg
(ttot, all_regi)
average efficiency growth across FE types x
p20_exponImi
(ttot, all_regi, all_in)
exponent of RD function x
p20_exponInno
(ttot, all_regi, all_in)
exponent of RD function x
q20_effGr
(ttot, all_regi, all_in)
R&D function x
q20_effImi
(ttot, all_regi, all_in)
efficiency improvement by imitation x
q20_effInno
(ttot, all_regi, all_in)
efficiency improvement by innovation x
v20_effImi
(ttot, all_regi, all_in)
efficiency improvement by imitation x
v20_effInno
(ttot, all_regi, all_in)
efficiency improvement by innovation x

Sets

sets in use
  description
all_in all inputs and outputs of the CES function
all_regi all regions
cesParameter parameters of the CES functions and for calibration
in(all_in) All inputs and outputs of the CES function
inRD20(all_in) Inputs included in extended endogenous growth
modules all the available modules
noRD(all_in) Inputs not included in endogenous growth
ppfEn(all_in) Primary production factors energy
regi(all_regi) all regions used in the solution process
t(ttot) modeling time, usually starting in 2005, but later for fixed delay runs
tall time index
ttot(tall) time index with spin up

Authors

Marian Leimbach, Lavinia Baumstark

See Also

01_macro, 29_CES_parameters, 36_buildings, 37_industry, 80_optimization, core

References